# Homogeneous Yield r-g Analysis (23-Country Bond Yield Sample)

Addresses concern that r-g "null" depends on heterogeneous rate measures.
All three regressions estimated on identical sample of countries with 10-year government bond yields.

## Panel Results (identical sample)

| Dependent Variable | Z₁ Coefficient | SE | p-value | N | Countries | R² |
|:--|--:|--:|--:|--:|--:|--:|
| 10y Bond Yield | 53.07** | 20.72 | 0.0107 | 635 | 23 | 0.225 |
| Real GDP Growth | 35.60*** | 12.88 | 0.0059 | 635 | 23 | 0.193 |
| r-g (bond yield) | 20.07 | 28.18 | 0.4766 | 635 | 23 | 0.170 |

## Formal Equality Test

The r-g regression constitutes a direct test of H₀: β_rate = β_growth.

- β_rate (Z₁) = 53.07 (SE = 20.72)
- β_growth (Z₁) = 35.60 (SE = 12.88)
- β_rate − β_growth = 17.47 (approx. SE = 24.40)
- Approximate t = 0.716, p = 0.4742
- Direct r-g regression: Z₁ = 20.07 (p = 0.4766)

## Interpretation

We do not find robust evidence that demographics move r-g, even on a homogeneous sample of 23 countries with 10-year government bond yields. The demographic effects on interest rates and growth approximately cancel.